Anyone can answer this question, but I am particularly interested in hearing from people with a knowledge of northern Virginia geography.

For the Union, much of the focus of the Civil War was attacking and capturing the Confederate capital of Richmond, Virginia.

Early in the war, the North's General McClellan waged the brilliantly conceived but poorly executed Peninsula campaign from the coast using seapower, but he was the exception.

After this campaign and the battle of Antietam, McClellan's successors preferred to swing west through Fredericksburg (Burnside), Chancellorsville (Hooker), and the Wilderness (Grant). This was true even though the terrain favored the Confederates (who won all three above-mentioned battles).

What made this route (through the same general area) so attractive to different Union generals?

Not "answering" until I have a chance to consult some maps, but my understanding was always that this was the most direct overland route between DC and Richmond (the route the roads took). To take any other path (besides McClellan's seaborne route) would be to expose your supply lines to enemy counter-attacks along those same roads. Do I have that wrong?
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T.E.D.♦Sep 4 '13 at 14:29

Oh, an upvote for a really interesting question, and a virtual upvote for pointing out the dichotomy between McClellan's strategic chops and his tactical chops.
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T.E.D.♦Sep 4 '13 at 14:33

Besides finding a way to not* get caught with half an army on each side of the Potomac? Lee would never had had to fight Gettysburg if any Union commander got caught with the Potomac running through his army.
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Pieter GeerkensSep 5 '13 at 0:31

@Tea Drinker: Did the English Civil War also have a Union Army approaching a Richmond from via Western Route.
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Pieter GeerkensJan 11 '14 at 22:36

3 Answers
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It is a mistake to think of the Battle of the Wilderness as a Confederate Victory. While it is true that Union losses exceeded Confederate losses, Grant could replenish his and Lee couldn't. Lee had to destroy the Union army to win, and Grant just had to wear Lee down.

Further, though Grant vacated the battlefield following the battle, he advanced rather than retreating. Lee then had to abandon the battlefield as well to cover Richmond.

Many authors have described the tremendous boost to Union morale that ensued from Grant's actions after the battle. Here is one account (from Wikipedia, because it is on-line and convenient):

Both flanks had been badly bruised, and [Grant's] 17,500 casualties in two days exceeded the Confederate total by at least 7,000. Under such circumstances previous Union commanders in Virginia had withdrawn behind the nearest river. Men in the ranks expected the same thing to happen again. But Grant had told Lincoln "whatever happens, there will be no turning back."

While the armies skirmished warily on May 7, Grant prepared to march around Lee's right during the night to seize the crossroads village of Spotsylvania a dozen miles to the south. If successful, this move would place the Union army closer to Richmond than the enemy and force Lee to fight or retreat. All day Union supply wagons and the reserve artillery moved to the rear, confirming the soldiers' weary expectation of retreat. After dark the blue divisions pulled out one by one.

But instead of heading north, they turned south. A mental sunburst brightened their minds. It was not another "Chancellorsville ... another skedaddle" after all. "Our spirits rose," recalled one veteran who remembered this moment as a turning point in the war. Despite the terrors of the past three days and those to come, "we marched free. The men began to sing." For the first time in a Virginia campaign the Army of the Potomac stayed on the offensive after its initial battle

— James M. McPherson, Battle Cry of Freedom

By another account that I have read, but cannot locate just now, Grant himself stood all night long at the key crossroads, in a dark Union overcoat and smoking a pipe, directing all the traffic South instead of North.

The true victor of a battle is the general who retains the strategic initiative after the battle. All secondary indications of victory, such as casualty figures, prisoners and captured munitions, can authoritatively be summarized in this simple assessment. The whole point of war, and of battle, is to impose one's will on the enemy, and ultimately to leverage this into a destruction of the enemy's resistance to this imposition.

Grant achieved this in The Wilderness in spades, casualty figures be damned.

Further, it is important to recognize that while Washington was the capitol of the North, Richmond was the heart and soul of the Confederacy in many ways, as well as its capitol. The loss of Washington, like the loss of Moscow in 1812, would have been a handicap but not an amputation of the North's ability to continue the war.

Contrariwise, the South could only win by retaining its territorial integrity long enough to exhaust the Union's will to fight. With each loss of territory, the South was incrementally shaved of its already tenuous ability to maintain an army in the field, and thus to continue fighting the war.

Update (just for Lennart Regebro):
A quick comparison on Google Earth shows that the Potomac River at Harper's Ferry is roughly the same width as the Danube channels from Lobau Island to Aspern-Essling; The scale on Google Earth suggests about 400-450 feet, but I have reason to believe that may actually be about double the real figure. The Potomac does get narrower near Brunswick, by about 1/3, but from the appearance also faster and deeper.

The Rappahannock is perhaps just half the width of the Potomac, but that is still a non-trivial obstacle.

Given the difficulty of forcing a river crossing against determined opposition, it seems natural that a both sides would attempt stealth and maneuver as means of achieving a crossing.

Also, a quick glance at a map (such as this or many others available on the web) shows that Fredericksburg and Chancellorsville are far from being western routes to Richmond. In fact, unless one wishes to paddle down the length of a multi-mile wide Potomac due south of Washington, it would be difficult to find any major city on the Rappahannock remotely closer to a direct bee-line between Washington and Richmond to name a battle after.

Given this, one could easily argue that Grant choose the Wilderness route because Meade, Hooker, McClennan and Scott (did I miss any) had amply demonstrated the foolishness of attempting anything more direct.

I was going to ask the question, but maybe you know the answer: What caused the French to stiffen after the (1709) battle of Malpalquet? Was it the 20,000 casualties for the Allies vs. only 11,000 for the French, or was it because the Dutch suffered 5,000-6,000 of the Allied casualties.
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Tom AuSep 5 '13 at 1:34

That's an era I have not studied much. A quick perusal of Wikipedia on The War of Spanish Succession suggests that perhaps Marlborough was a McClellan, rather than a Grant, in the final analysis. More troops fought at Malpalquet than did at Waterloo 106 years later, with proportionally more casualties than commanders and nations were then familiar with. In one sense, it may just have been a type of sticker shock for Marlborough and his allies.
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Pieter GeerkensSep 5 '13 at 1:48

I just spotted an excerpt from the letter Villars wrote to Louis XIV after the battle, in which he rejoices that just one more such battle loss would win the war! (Because of the lopsidedness of the casualties, even though Villars was ejected from the battlefield.)
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Pieter GeerkensSep 5 '13 at 1:51

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This answer is very interesting, but I don't see how it even attempts to answer the question.
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Lennart RegebroSep 5 '13 at 14:28

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@LennartRegebro: The answer is for the OP, as you note; the notification was a whorish solicitation of your up-vote. ;-)
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Pieter GeerkensSep 6 '13 at 2:37

Fredericksburg is directly North of Richmond on the direct road to Washington. So an army here covers movements against the capital. But crossing the numerous rivers in Virginia at this point and east is complicated because they are much wider.

If you go west, around Culpeper, you have a railroad (The Orange and Alexandria iirc) to bring up supplies, and the rivers are smaller and more crossable.

Any farther west, or east water routes like the Peninsular campaign and you don't cover Washington DC and have to divide your army to do so.

So the basic answer is that there are only two land routes in the space available, and the Union used both at different times.

...and they even tried a water-route once.
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T.E.D.♦Jan 10 '14 at 0:00

Twice, if you consider the Butler expedition towards Richmond about the time of the Wilderness battle. But, yes, all of the practical lines were used or considered at the time.
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OldcatJan 10 '14 at 0:06

One reason appears to be the success of (Confederate) General Stonewall Jackson's Shenandoah Valley Campaign in late spring of 1862.

Using hit and run tactics, Jackson took on, and defeated four slightly weaker forces in northern Virginia totalling 52,000 men, with only 17,000 of his own. These 52,000 men, most of which had originally been intended as reinforcements for McClellan, were instead held back to defend the approaches to Washington D.C. They formed the (Union) Army of Virginia.

Jackson managed to be in "two places at once." That is, his 17,000 reinforcement of Robert E. Lee near Richmond, brought Lee's total strength to about 90,000 men, versus about 100,000 for McClellan. But Jackson's (earlier) and "virtual" presence in northern Virginia prevented his former opponents from reinforcing McClellan by 52,000 men, which led to the latter's (nominal) defeat in the Peninsula Campaign. It's doubtful that even Ulysees S. Grant could have beaten Lee with only a 10 to 9 numerical preponderance.

John Pope, a commander with some success in the West, was given overall command of the Army of Virginia of 52,000 men, and offered McClellan's 100,000 men as reinforcements, provided that he kept the combined army between northern Virginia and Richmond (basically the western route). Pope agreed, but was defeated before he received more than a handful of reinforcements from the Army of the Potomac. McClellan was given a second chance at command, but henceforth, Union generals could use the Army of Virginia only along the western route, and not the eastern (Peninsula) route. Which is why they chose the western route.